Week 2 - Regression and model validation
Read the data
rm(list = ls()) # clear workspace first
learning2014 <- read.csv("~/Documents/GitHub/IODS-project/learning2014.csv") # my own data wrangling
# read.table("~/Documents/GitHub/IODS-project/data/learning2014.txt", sep = ",") # Kimmo's dataExplore the structure and dimensions of the dataset
str(learning2014)## 'data.frame': 166 obs. of 7 variables:
## $ gender : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
## $ Age : int 53 55 49 53 49 38 50 37 37 42 ...
## $ Attitude: int 37 31 25 35 37 38 35 29 38 21 ...
## $ deep : num 3.58 2.92 3.5 3.5 3.67 ...
## $ stra : num 3.38 2.75 3.62 3.12 3.62 ...
## $ surf : num 2.58 3.17 2.25 2.25 2.83 ...
## $ Points : int 25 12 24 10 22 21 21 31 24 26 ...dim(learning2014)## [1] 166 7The data includes 7 variables and 166 observations. The variables are: 1. Gender (Female = 1 Male = 2) 2. Age 3. Attitude 4-6. Mean scores of the deep, strategic and surface learning 7. Exam points
library(ggplot2) # Access the gglot2 libraryShow a graphical overview of the data
# show gender distributions as bar graph
p1 <- ggplot(learning2014, aes(gender))
p1 + geom_bar()
# display variable distributions as histogram
p2 <- ggplot(learning2014, aes(Age))
p2 + geom_histogram(binwidth = 5)
p3 <- ggplot(learning2014, aes(Attitude))
p3 + geom_histogram(binwidth = 2)
p4 <- ggplot(learning2014, aes(deep))
p4 + geom_histogram(binwidth = 0.5)
p5 <- ggplot(learning2014, aes(stra))
p5 + geom_histogram(binwidth = 0.5)
p6 <- ggplot(learning2014, aes(surf))
p6 + geom_histogram(binwidth = 0.5)
p7 <- ggplot(learning2014, aes(Points))
p7 + geom_histogram(binwidth = 2)
# show relationships between variables
p8 <- ggplot(learning2014, aes(x = Attitude, y = Points, col=gender))
p8 + geom_point() + ggtitle("Relationship between exam points and deep learning") + geom_smooth(method = "lm")
p9 <- ggplot(learning2014, aes(x = deep, y = Points, col=gender))
p9 + geom_point() + ggtitle("Relationship between exam points and deep learning") + geom_smooth(method = "lm")
p10 <- ggplot(learning2014, aes(x = stra, y = Points, col=gender))
p10 + geom_point() + ggtitle("Relationship between exam points and strategic learning") + geom_smooth(method = "lm")
p11 <- ggplot(learning2014, aes(x = surf, y = Points, col=gender))
p11 + geom_point() + ggtitle("Relationship between exam points and surface learning") + geom_smooth(method = "lm")
p12 <- ggplot(learning2014, aes(x = Age, y = Points, col=gender))
p12 + geom_point() + ggtitle("Relationship between age and exam points") + geom_smooth(method = "lm")
p13 <- ggplot(learning2014, aes(x = Age, y = Attitude, col=gender))
p13 + geom_point() + ggtitle("Relationship between age and attitudes") + geom_smooth(method = "lm")
library(GGally)
pairs(learning2014[-1], col = learning2014$gender)
p <- ggpairs(learning2014, mapping = aes(col=gender, alpha = 0.3), lower = list(combo = wrap("facethist", bins = 20)))
# draw the plot
p
Summary of the variables
summary(learning2014)## gender Age Attitude deep stra
## F:110 Min. :17.00 Min. :14.00 Min. :1.583 Min. :1.250
## M: 56 1st Qu.:21.00 1st Qu.:26.00 1st Qu.:3.333 1st Qu.:2.625
## Median :22.00 Median :32.00 Median :3.667 Median :3.188
## Mean :25.51 Mean :31.43 Mean :3.680 Mean :3.121
## 3rd Qu.:27.00 3rd Qu.:37.00 3rd Qu.:4.083 3rd Qu.:3.625
## Max. :55.00 Max. :50.00 Max. :4.917 Max. :5.000
## surf Points
## Min. :1.583 Min. : 7.00
## 1st Qu.:2.417 1st Qu.:19.00
## Median :2.833 Median :23.00
## Mean :2.787 Mean :22.72
## 3rd Qu.:3.167 3rd Qu.:27.75
## Max. :4.333 Max. :33.00# another way of summarising the variables
#library(dplyr)
#learning2014 %>%
# group_by(gender) %>%
# summarise(mean = mean(Attitude), n = n())The sample consist of mainly female participants. The majority of participants are between 20 to 30 years old. The variables are mostly normally distributed. The attitudes predict the exam points, but the learning strategies do not explain the exam points. Age does not explain the exam points or attitudes.
Fitting of a regression model to study whether attitudes, strategic and surface learning strategies explain the exam points. The learning strategies (strategic and surface) did not explain the exam points significantly. The exam points were significantly (p = 4.12e-09) explained by attitudes
# fit a linear model
my_model1 <- lm(Points ~ Attitude + stra + surf, data = learning2014) # how to use three explanatory vars
summary(my_model1)##
## Call:
## lm(formula = Points ~ Attitude + stra + surf, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.1550 -3.4346 0.5156 3.6401 10.8952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.01711 3.68375 2.991 0.00322 **
## Attitude 0.33952 0.05741 5.913 1.93e-08 ***
## stra 0.85313 0.54159 1.575 0.11716
## surf -0.58607 0.80138 -0.731 0.46563
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.296 on 162 degrees of freedom
## Multiple R-squared: 0.2074, Adjusted R-squared: 0.1927
## F-statistic: 14.13 on 3 and 162 DF, p-value: 3.156e-08my_model2 <- lm(Points ~ Attitude, data = learning2014)
summary(my_model2)##
## Call:
## lm(formula = Points ~ Attitude, data = learning2014)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.9763 -3.2119 0.4339 4.1534 10.6645
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.63715 1.83035 6.358 1.95e-09 ***
## Attitude 0.35255 0.05674 6.214 4.12e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.32 on 164 degrees of freedom
## Multiple R-squared: 0.1906, Adjusted R-squared: 0.1856
## F-statistic: 38.61 on 1 and 164 DF, p-value: 4.119e-09Produce the diagnostic plots: Residuals vs Fitted values, Normal QQ-plot and Residuals vs Leverage
plot(my_model2)
